This paper identifies and discusses misconceptions that students have in making judgments of center and variability when data are presented graphically. An assessment addressing interpreting center and variability in histograms and stem-and-leaf plots was administered to, and follow-up interviews were conducted with, undergraduates enrolled in introductory statistics courses. Assessment items focused upon comparing the variability of two data sets of common range represented by bell-shaped histograms on a common scale, computing measures of center from data extracted from graphs, and in comparing the relative location of the mean and median on a histogram from skewed data. Students' misconceptions often stemmed from their difficulty in maintaining understanding of the data that are being represented graphically.

Recognizing and interpreting variability in data lies at the heart of statistical reasoning. Since graphical displays should facilitate communication about data, statistical literacy should include an understanding of how variability in data can be gleaned from a graph. This paper identifies several types of graphs that students typically encounter-histograms, distribution bar graphs, and value bar charts. These graphs all share the superficial similarity of employing bars, and yet the methods to perceive variability in the data differ dramatically. We provide comparisons within each graph type for the purpose of developing insight into what variability means and how it is evident within the data's associated graph. We introduce graphical aids to visualize variability for histograms and value bar charts, which could easily be tied to numerical estimates of variability.

Contrived-rate problems, generally categorized as “work” problems, were a staple in commercial algebra textbooks of old.

The 2008 presidential election is a great backdrop for analyzing graphs, learning about population distributions, and studying the effect on the electoral voting process.